Have you messed around as the root user before and actually installed applications as root? I know on Unix systems that if an application is installed as root, with certain flags present, the permissions and file paths become set such that only root has access to some of the components needed to run the application. I've seen this happen in SAP when root is used to install components because the person doing the installation doesn't like that the sapadm or oraadm user has to keep typing in "sudo command" every few minutes. The install works, but won't run right because log files, binaries, etc are all owned by the wrong user/group or pathed to the wrong home directory. I've also seen where components were installed in a "root" or system directory instead of a user or common directory. The base directory structure ends up prohibiting others from using those applications because, while permissions are correct on some files, not everything is accessible at the directory level.

Short of it... sounds to me like root or a member of another group owns parts of your applications, was probably used to install certain things, may have altered base permissions on files used by other applications in general, or that those applications are using directories and files they have no access to in their course of operations. Alternatively, your regular user account could also be a member of some obscure or custom group that doesn't play well with "normal" installations.

You may wish to try downloading the an application that doesn't work all over again (as root if you can't as your regular user). While still root, just change the permissions to something like 777 or 775 and make sure the group is "admin" or "staff" and not "wheel" or "system". Place the installer in a common directory, or better yet your main user's home directory. Then log out of the root account and log back in as your user. Try the installation again. If it works properly this time, then we are on the right track. If it doesn't then it could mean that something is services or the like is buggered up.

Never judge a man, untill you have walked a mile in his shoes...
That way you'll be a mile away from him, and you'll have his shoes.